We have been given that in triangle ABC angle A=45 angle B =40 and a=7. We are asked to find the equation that we can use to solve for 'f'.
We have two angles and opposite sides to these angles.
We will use Law of Sines to solve our given problem.
, where a, b and c are opposite sides corresponding to angles A, B, and C respectively.
The angle opposite to side b is 40 degrees and angle opposite to side a is 45 degrees.
Upon substituting these values in Law of Sines, we will get:
Therefore, our required equation would be .
Step-by-step explanation:
Both equations have a term in them, so if we subtract the second equation from the first, it will eliminate those terms, allowing us to solve for the remaining terms:
Finally, we can plug this value for into either of the two original equations to solve for :
This means the solution to the system of equations is .
1.
cos(90-x) = sin(x)
sin(-x) = -sin(x)
cos²(180+x) = (-cos²x) = cos²(x)
Then
cos(90-x) .sin(-x)/cos²(180+x) = sin(x).(-sin(x))/cos²(x)
= -sin²(x))/cos²(x)
= −tan²(x)
2.
tan² (360° + θ)/cos(90° + θ).sin(180° - θ)
tan² (360° + θ) = tan² (θ)
cos(90° +x) = - sin(θ)
sin(180° - θ) = sin(θ)
tan² (360° + θ)/cos(90° +θ).sin(180° - θ) = tan² (θ)/- sin(θ) sin(θ)
= -tan²(θ)/sin²(θ)
= -1/cos²(θ)
= - (cos²θ + sin²θ)/cos²θ
= -1 - tan²θ
34-5x+2(x-2)=15 1st get rid of () by distributing the 2.
34-5x+2x-4=15 Now collect like terms.
30-3x=15 Get -3x by itself by subtracting 30 in both sides.
-3x=-15 You want X by itself so divide by -3 on both sides.
x=5